Math Mutation 84: How To Bankrupt Your Boss And Get Rich With all the econmic turmoil in the news lately, I've been leafing again through my copy of "Fooled By Randomness", Nassim Taleb's excellent book about basic probability fallacies that impact modern investors. One important topic in there, that I think may be very relevant to the current situation, is the concept of asymmetric bets. It's not a very complex concept msathematically, but it's still one that a surprising number of people fail to think through when investing. Suppose I were to tell you that mathmuation.com stock has a 90% chance of going up in the next year, and only a 10% chance of going down. For the moment assume we have completely accurate information, so you are sure that these probabilities are correct. Your instinct might be to go out and buy a bunch of shares. After all, there is a 90% chance that you are going to make a profit. But is this the correct answer? Actually, you still need more information to figure out whether the stock is something you should buy or should sell. To see this, let's assume the stock value is currently 100 dollars, and look at the expected profit from buying a share in two scenarios. In scenario one, if the stock either rises or falls, it will be by fifty cents. So if we buy a share, our expected gain is .9 times 50 cents + .1 times (minus fifty) cents, for a total of + 40 cents. Thus, due to the positive expected gain, this is a buy-- in the long term, you expect on average to gain money when buying in this scenario. Now let's look at another scenario. Here, the 90% chance of a rise is due to slowly spreading word-of-mouth about Math Mutation, so if the stock goes up, it will still be about fifty cents. However, the 10% chance of a fall is due to rumors that the host will soon convert to the Amish religion and give up all technology, so there will be no further episodes and the podcast will be worthless, and the stock will drop by the full 100 dollars. Then your expected gain will be .9 times 50 cents plus .1 times (minus 100) dollars, for a total of minus nine dollars and fifty-five cents. In the long term, using this strategy repeatedly and deciding to buy the stock, you expect a net loss. This is an example of an asymmetric bet-- while there is a larger chance of a gain, the magnitude of the gain is not enough to justify the risk of the huge loss. Even though there is a 90% chance of the stock going up, the one in ten times it goes down will be such a catastrophe that it will wipe out all your previous gains, and more. So it seems like an intelligent investor should always try to recognize such asymmetic bets, and make the rational decision not to invest if there is a large chance of a small gain, but a small chance of an overwhelming loss like this, right? Well, we need to add one more twist. Suppose you are managing a huge corporate portfolio worth hundreds of millions of dollars. Each year in which the corporate account gains, you get a half-million dollar bonus, which you can then put in a personal savings account. However, if the corporate account goes bankrupt, you will be fired. Now think again about the asymmetric bet. If there is a 90% chance that it will gain, then you know you can place this bet for your company-- nine out of ten years, you will get a huge bonus. Eventually you will probably bankrupt the company and get fired, but by then you will have squirreled away enough bonuses from your successful years that you won't care. In fact, you probably have a decent-looking resume for applying to further financial jobs, with a record superficially showing that most of the time, you made money for your company. Now of course, I don't know enough details to say whether this is what actually happened in any of the recent crises. In his book, Taleb does describe many examples of individual traders who seem to be doing well for a number of years, then suddenly lose their companies a huge amount of money that dwarfs the total of their previous gains. And recent additions to Taleb's website, linked in the show notes, seem to indicate that he thinks his ideas applied directly to Fannie Mae. In any case, in the current situation, it does seem suspicious to me that there are so many cases where individual executives exited with millions of dollars, while leaving behind bankrupt companies for the taxpayers to bail out. But what do I know, I'm just a podcaster. And this has been your math mutation for today. References:
  • Taleb's website, fooledbyrandomness.com